热流耦合井筒流动及其地层渗流研究
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摘要
在石油勘探与开发中,通过对井底瞬时压力的反演可以了解地层中油气储量、渗透性及井壁污染等参数。由于压力和温度有很多相似之处,本文开展了对井底瞬时温度的解释反演研究以及温度效应对压力试井解释的影响与修正的研究。这样,一方面可以有效使用温度数据,另一方面在进行试井解释和储层评价时弥补了压力试井的不足。而且井筒中温度分布的准确预测是油气井设计和动态分析的重要基础,对提高采油设备的设计水平、改进油井加热方法以及地层参数计算和储油量评价等都有重要的指导意义。
本文对生产井或注入井井筒和地层的温度随时间变化进行了研究,考虑了多层地层条件下井筒和地层的换热,其中地层由n个不同的热力学及物理性质的多孔介质层组成,整个系统由井筒区、热表皮区(包括套管、环空、水泥环等)及地层三部分组成。其中地层中只有水平方向的热传导,忽略垂直方向上的热传导,井筒中仅考虑流体的热对流,忽略热传导。井筒和地层的温度通过综合热传导系数联系起来。对方程组进行拉氏变换,在拉氏空间上求解,再运用数学物理方程的理论进行反演,得到井筒温度和地层温度的解析解表达式,进一步得到了温度试井所需要的图版。通过将实测温度曲线与理论图版做拟合,对实测温度进行定量解释,可得分层注入量及地层热力学参数。
由于蒸汽热采会导致地层温度变化,从而使地层中流体性质发生变化,进而改变地层压力曲线的形态。本文提出一个蒸汽注采井的压力试井模型和曲线拟合方法,采用多区域径向复合油藏模型对地层进行划分,并从地层渗流方程出发得到多区域的压力扩散方程,对其进行拉氏变换,得到拉氏空间上的解,再经过反演得到压力的解析表达式,为了引入温度效应,需要对压力进行修正,于是本文引入了由温度效应引起的压力部分,得到考虑温度效应的多区域复合油藏压力典型曲线模版。在此基础上对一些实测压力曲线进行拟合,给出了解释结果。
由于气体压力随温度变化而变化,本文提出一个考虑热效应的气井压力模型并给出计算方法。该模型根据根据气体在井筒中流动的特点给出了气体流动的连续性方程、动量方程及能量方程,再根据气井生产状况的不同给出相应的定解条件。由于井底与产气层相连通,井底压力来源于气体在地层中的渗流方程。文中定义了气体渗流的拟压力,给出了拟压力的气体渗流方程,由叠加原理得出变流量条件下的气井井底拟压力的半数值半解析表达式,该表达式作为井筒流动的一个边界条件。
由于井底压力来源于地层,而井底压力随着时间和生产状态的变化(如变流量或关井)发生变化,因此采用井筒流动与地层渗流耦合迭代求解,即对地层渗流采用半解析半数值进行求解,渗流方程在井壁的压力分布作为井简的底部压力边界条件,井筒流动方程采用PISO(Pressure Implicit with Splitting of Operators)数值求解,从而得到井筒中压力及速度分布,井底速度转化为流量后作为地层渗流的流量条件,这样不断迭代直至收敛,得到井筒流动及地层渗流的压力分布和速度分布。计算结果表明：热效应对井底压力曲线的早期形态影响较大,从而解释了实测气井压力曲线早期数据“异常”这一现象,不仅丰富和发展了现代试井理论,而且对地层的认识更加准确。
In the exploration and exploitation of petroleum, many parameters such as oil and gas reserves, permeability in the reservoir and wellbore damage, can be known through the inversion of instant pressure at bottom hole of the well. Since temperature has much in common with pressure, research of interpretation and inversion on instant temperature at bottom hole and research on the influence and correction of temperature on pressure well test are launched in this paper. Thus, the temperature data is effectively used and deficiency of pressure well test is made up. The correct prediction of temperature profile in well bore is the important basis of oil-gas well design and dynamic analysis, it also has directive significance in many aspects of oil gas field.
In this paper, the varing temperature of wellbore and formation in injection well or producing well with time is researched. The formation consists of many layers, which have different thermodynamics properties. The whole system consists of wellbore zone, thermal skin zone and formation zone. In the formation there is only horizontal thermal exchange with vertical thermal exchange ignored. In the wellbore there is only heat convection with heat conduction ignored. Wellbore and formation are connected by Ramey heat-transfer coefficient. Laplace transform is used to solve the equations, after inversion, an analytical solution of temperature in wellbore and formation is obtained and further, typical temperature well testing curves are obtained. Then the measured temperature data can be used to fit the typical temperature well testing curves. Now the measured temperature data can be qualitatively interpretated and some thermal parameters of formation can be obtained.
Because steam injection changes the temperature of reservoir, so the properties of fluid in reservoir and shape of pressure curves in reservoir is changed. A pressure test model and curve fitting method in steam injection well is presented. A multi-area radial composite reservoirs model is used to classify strata. Laplace transform is used to get the analytical solution. In this paper, the correction of pressure by temperature is realized through gas equation of state. After the pressure is corrected, typical pressure well testing curves are obtained. the measured pressure data can be used to fit the typical pressure well testing curves. Some actual examples are given here and corresponding interpretation results are also given.
Considering that gas temperature has obvious influence on pressure, a pressure model with thermal effect considered in gas well is established here, which gives the governing equations for pipe flow in wellbore and seepage equations of the real gas in reservoir. In seepage equation pseudo-pressure is imported,and according to boundry conditions and initial conditions, a half-analytic and half-numerical expression of bottomhole pressure of variable-flowrate gas well is obtained through superposition principle, which is the pressure boundry condition for pipe flow in wellbore.
The Bottomhole pressure varies with time and producing state,and it's connected to reservoir. So pipe flow in wellbore and seepage in reservoir must be coupled,and solved iteratively. PISO(Pressure Implicit with Splitting of Operators) method is used to solve wellbore governing equations. By solving wellbore governing equations bottomhole flowrate is obtained,which is the input parameter for seepage equations in reservoir. The iteration must keep running to achieve convergence. Then distribution of temperature and pressure is obtained. The result of calculation shows that thermal effect has great influence on the early shape of the pressure well-test curve, which gives a explaination of exceptional behavior of measured pressure data in early period and will not only enrich modern welltest theory but also give a better understanding of reservoir.
本文对生产井或注入井井筒和地层的温度随时间变化进行了研究,考虑了多层地层条件下井筒和地层的换热,其中地层由n个不同的热力学及物理性质的多孔介质层组成,整个系统由井筒区、热表皮区(包括套管、环空、水泥环等)及地层三部分组成。其中地层中只有水平方向的热传导,忽略垂直方向上的热传导,井筒中仅考虑流体的热对流,忽略热传导。井筒和地层的温度通过综合热传导系数联系起来。对方程组进行拉氏变换,在拉氏空间上求解,再运用数学物理方程的理论进行反演,得到井筒温度和地层温度的解析解表达式,进一步得到了温度试井所需要的图版。通过将实测温度曲线与理论图版做拟合,对实测温度进行定量解释,可得分层注入量及地层热力学参数。
由于蒸汽热采会导致地层温度变化,从而使地层中流体性质发生变化,进而改变地层压力曲线的形态。本文提出一个蒸汽注采井的压力试井模型和曲线拟合方法,采用多区域径向复合油藏模型对地层进行划分,并从地层渗流方程出发得到多区域的压力扩散方程,对其进行拉氏变换,得到拉氏空间上的解,再经过反演得到压力的解析表达式,为了引入温度效应,需要对压力进行修正,于是本文引入了由温度效应引起的压力部分,得到考虑温度效应的多区域复合油藏压力典型曲线模版。在此基础上对一些实测压力曲线进行拟合,给出了解释结果。
由于气体压力随温度变化而变化,本文提出一个考虑热效应的气井压力模型并给出计算方法。该模型根据根据气体在井筒中流动的特点给出了气体流动的连续性方程、动量方程及能量方程,再根据气井生产状况的不同给出相应的定解条件。由于井底与产气层相连通,井底压力来源于气体在地层中的渗流方程。文中定义了气体渗流的拟压力,给出了拟压力的气体渗流方程,由叠加原理得出变流量条件下的气井井底拟压力的半数值半解析表达式,该表达式作为井筒流动的一个边界条件。
由于井底压力来源于地层,而井底压力随着时间和生产状态的变化(如变流量或关井)发生变化,因此采用井筒流动与地层渗流耦合迭代求解,即对地层渗流采用半解析半数值进行求解,渗流方程在井壁的压力分布作为井简的底部压力边界条件,井筒流动方程采用PISO(Pressure Implicit with Splitting of Operators)数值求解,从而得到井筒中压力及速度分布,井底速度转化为流量后作为地层渗流的流量条件,这样不断迭代直至收敛,得到井筒流动及地层渗流的压力分布和速度分布。计算结果表明：热效应对井底压力曲线的早期形态影响较大,从而解释了实测气井压力曲线早期数据“异常”这一现象,不仅丰富和发展了现代试井理论,而且对地层的认识更加准确。
In the exploration and exploitation of petroleum, many parameters such as oil and gas reserves, permeability in the reservoir and wellbore damage, can be known through the inversion of instant pressure at bottom hole of the well. Since temperature has much in common with pressure, research of interpretation and inversion on instant temperature at bottom hole and research on the influence and correction of temperature on pressure well test are launched in this paper. Thus, the temperature data is effectively used and deficiency of pressure well test is made up. The correct prediction of temperature profile in well bore is the important basis of oil-gas well design and dynamic analysis, it also has directive significance in many aspects of oil gas field.
In this paper, the varing temperature of wellbore and formation in injection well or producing well with time is researched. The formation consists of many layers, which have different thermodynamics properties. The whole system consists of wellbore zone, thermal skin zone and formation zone. In the formation there is only horizontal thermal exchange with vertical thermal exchange ignored. In the wellbore there is only heat convection with heat conduction ignored. Wellbore and formation are connected by Ramey heat-transfer coefficient. Laplace transform is used to solve the equations, after inversion, an analytical solution of temperature in wellbore and formation is obtained and further, typical temperature well testing curves are obtained. Then the measured temperature data can be used to fit the typical temperature well testing curves. Now the measured temperature data can be qualitatively interpretated and some thermal parameters of formation can be obtained.
Because steam injection changes the temperature of reservoir, so the properties of fluid in reservoir and shape of pressure curves in reservoir is changed. A pressure test model and curve fitting method in steam injection well is presented. A multi-area radial composite reservoirs model is used to classify strata. Laplace transform is used to get the analytical solution. In this paper, the correction of pressure by temperature is realized through gas equation of state. After the pressure is corrected, typical pressure well testing curves are obtained. the measured pressure data can be used to fit the typical pressure well testing curves. Some actual examples are given here and corresponding interpretation results are also given.
Considering that gas temperature has obvious influence on pressure, a pressure model with thermal effect considered in gas well is established here, which gives the governing equations for pipe flow in wellbore and seepage equations of the real gas in reservoir. In seepage equation pseudo-pressure is imported,and according to boundry conditions and initial conditions, a half-analytic and half-numerical expression of bottomhole pressure of variable-flowrate gas well is obtained through superposition principle, which is the pressure boundry condition for pipe flow in wellbore.
The Bottomhole pressure varies with time and producing state,and it's connected to reservoir. So pipe flow in wellbore and seepage in reservoir must be coupled,and solved iteratively. PISO(Pressure Implicit with Splitting of Operators) method is used to solve wellbore governing equations. By solving wellbore governing equations bottomhole flowrate is obtained,which is the input parameter for seepage equations in reservoir. The iteration must keep running to achieve convergence. Then distribution of temperature and pressure is obtained. The result of calculation shows that thermal effect has great influence on the early shape of the pressure well-test curve, which gives a explaination of exceptional behavior of measured pressure data in early period and will not only enrich modern welltest theory but also give a better understanding of reservoir.
引文
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